Hi I'm tying to understand notations in Integration, and would really appreciate some help making sure that my understanding is right. My books writes Let u and v be functions of x whose domains are an open interval I, and suppose du and dv exist for every x in I. Then it defines 1) ∫(du)= u + C 2) ∫(c*du) = c*∫(du) and 3) ∫(cos(u)du = sin u +C Now i do understand the first 2, but I want to make sure i understand the 3rd rule. If u is a function of x with the equation u(x)=x^2 Then the derivative du/dx= 2x The differential du=u'(x)dx Now if it's true that du=u'(x)dx Then it does make sense that ∫du =u+C because ∫du=∫u'(x)*dx and the integral of the derivative if u is u. But if u=x^2 Then ∫(cos(x^2)*du = ∫(cos(x^2)*(2x)dx and this is = sin(x^2) + C as the statement above says. because the derivative of sin(x^2) = cos(x^2)*(2x). Is this the right interpretation?